Fuzzification of set inclusion: theory and applications
Fuzzy Sets and Systems
A probabilistic and statistical view of fuzzy methods
Technometrics
Fuzzy Sets and Systems
On the variance of fuzzy random variables
Fuzzy Sets and Systems
Inclusion grade and fuzzy implication operators
Fuzzy Sets and Systems
Fuzzy Systems for Management
An alternative approach to fuzzy control charts: Direct fuzzy approach
Information Sciences: an International Journal
Probabilistic foundations for measurement modelling with fuzzy random variables
Fuzzy Sets and Systems
About approximate inclusion and its axiomatization
Fuzzy Sets and Systems
Fuzzy process control: construction of control charts with fuzzy numbers
Fuzzy Sets and Systems
On the variability of the concept of variance for fuzzy random variables
IEEE Transactions on Fuzzy Systems
The median of a random fuzzy number. The 1-norm distance approach
Fuzzy Sets and Systems
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The two most significant sources of uncertainty are randomness and incomplete information. In real systems, we wish to monitor processes in the presence of these two kinds of uncertainty. This paper aims to construct a fuzzy statistical control chart that can explain existing fuzziness in data while considering the essential variability between observations. The proposed control chart is an extension of Shewhart X@?-S^2 control charts in fuzzy space. The proposed control chart avoids defuzzification methods such as fuzzy mean, fuzzy mode, fuzzy midrange, and fuzzy median. It is well known that using different representative values may cause different conclusions to be drawn about the process and vague observations to be reduced to exact numbers, thereby reducing the informational content of the original fuzzy sets. The out-of-control states are determined based on a fuzzy in-control region and a simple and precise graded exclusion measure that determines the degree to which fuzzy subgroups are excluded from the fuzzy in-control region. The proposed chart is illustrated with a numerical example.